SOLUTION: you want to invest 10,000 dollars. how long will it take to double your investment at an annual interest rate of 10% compounded continuously?(round your answer to the nearest year

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Question 885944: you want to invest 10,000 dollars. how long will it take to double your investment at an annual interest rate of 10% compounded continuously?(round your answer to the nearest year)
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Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
One fast shortcut is the rule of 72. Divide 72 by 10 (ignore the percent) to get 72/10 = 7.2


So it takes roughly 7.2 years


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Let's use the formula to get a more accurate answer:


A = P*e^(r*t)

20000 = 10000*e^(0.10*t)

20000/10000 = e^(0.10*t)

2 = e^(0.10*t)

ln(2) = ln(e^(0.10*t))

ln(2) = 0.10*t*ln(e)

ln(2) = 0.10*t*1

ln(2) = 0.10*t

0.10*t = ln(2)

t = ln(2)/0.10

t = 6.93147180559946

t = 7 ... round to the nearest whole number


So it takes approximately 7 years (which is reasonably close to 7.2)


The final answer is 7 since they want you to use the formula and round to the nearest year. However, it's always good to know a fast shortcut such as the rule of 72.